Issue 42: Estimating Material Properties for Fire Modeling
By Marc Janssens, Ph.D., FSFPE
In a paper published more than 10 years ago, Babrauskas examined the question whether compartment fire models were good enough for Fire Safety Engineering (FSE).1 Babrauskas concluded that the main limitation of compartment fire models was that they generally were not capable of predicting fire growth, but only suitable for calculating the consequences of user-specified fires. Since the publication of Babrauskas' paper – in particular due to the continued development, accessibility and widespread use of field models such as FDS – significant progress has been made in the ability to model a fire. Room fire growth predictions involve the coupling of a compartment fire model and a pyrolysis model. The former calculates the thermal environment in the gas phase, while the latter quantifies the heat transfer and pyrolysis rate in the condensed phase.
METHODS TO PREDICT THE PYROLYSIS RATE OF A SOLID
Different approaches have been used to predict the onset (ignition) and rate of pyrolysis of a solid exposed in a compartment fire. Pyrolysis models can be grouped into four distinct categories based on the complexity of the model equations and the input data that are needed.
The most basic approach to predict the burning rate in a room fire is based on the assumption that the material behaves in the room as it does at a specified heat flux level in a bench-scale calorimeter such as the Cone Calorimeter or the Fire Propagation Apparatus. The method developed by Wickstrm and Gransson to predict fire growth in the standard ISO 9705 room/corner test is a good example of this approach.2 With this approach, the dynamic effects of the room fire on the exposure level are ignored while the dynamics of the heat release curve are largely maintained. The heat flux level is chosen so that it is a representative average (over space and time) for the fire scenario that is being modeled. 3
The empirical approach can be refined by using mass loss rate4 or heat release rate5 curves obtained at multiple heat fluxes. This makes it possible to account for the fact that the incident heat flux at different locations in the room varies with time.
Simple Analytical Models
A slightly more complicated approach determines the surface temperature of the material as a function of time based on (1) a simplified analytical solution of the one-dimensional transient heat conduction equation for a constant heat flux at the exposed surface, and (2) Duhamel's superposition theorem to account for changes in the heat flux as a function of time. The rate of surface temperature increase at a specified heat flux is a function of the thermal inertia of the material for the thermally thick (semi-infinite) case. The rate depends on the product of the thickness, density and specific heat capacity of the material for the thermally thin case.
The material is assumed to ignite once the surface temperature reaches a critical value. Following ignition the surface temperature is assumed to remain constant and the burning rate is determined from the net heat flux at the exposed surface and the heat of gasification of the material.6
Comprehensive Pyrolysis Models without Kinetics
Modeling of the condensed phase is greatly simplified if it is assumed that the conversion to volatiles and a solid residue (the latter for char-forming materials) occurs abruptly at a specified "pyrolysis temperature". One-dimensional pyrolysis can then be simulated as a phase-change problem using an integral model.7 This approach assumes that the heated depth varies as a function of time and that the temperature profile over this depth is a specified function (usually a polynomial) of the distance from the exposed surface. Based on these assumptions the partial differential heat conduction equation can be transformed into an ordinary differential equation. The material properties that are needed in this case are the thermal conductivity, density and specific heat capacity of the material (and of the solid residue for char-forming materials) and the heat of pyrolysis.
Comprehensive Pyrolysis Models with Kinetics
The pyrolysis models in this category are similar to those described in the previous section. The primary difference is that the pyrolysis is described as one or a combination of several finite rate reactions.8 Typically, an Arrhenius type expression is used to model the reaction kinetics. This greatly increases the complexity of the model and a finite element or finite difference method is therefore needed to solve the model equations.
Pyrolysis models in this category have several advantages. For example, they can be used to account for temperature effects on the thermal properties and to model the heat transfer in and pyrolysis of multi-layer three-dimensional objects. The trade-off is that additional testing is needed (typically thermogravimetric analysis) to obtain the kinetic parameters (reaction order, pre-exponential factor and activation energy) for each of the reactions.
NIST GRANT AND SFPE GUIDE
A detailed standard guide to instruct fire model users on how to obtain material input parameters consistent with pyrolysis model assumptions would be extremely helpful to the fire protection engineering community and would greatly facilitate consistent application of computer models. Numerous approaches to obtain material parameters for input into deterministic fire models have been published in the literature. A subset of these approaches is described in ASTM E 1591 Standard Guide for Obtaining Data for Deterministic Fire Models.9 Unfortunately, the ASTM guide is obsolete and incomplete as it was developed 15 years ago and only addresses input parameters for zone models.
Recognizing the importance and urgent need, the National Institute of Standards and Technology decided to fund the development of a new comprehensive guide. A grant was awarded to Worcester Polytechnic Institute (WPI) to lead this effort. WPI is supported by Southwest Research Institute (SwRI) and SFPE. A three-year project was initiated on July 1, 2008 and aims at developing a document that will serve as the basis for an SFPE guide on obtaining material properties for pyrolysis modeling. It is anticipated that a task group will be formed in 2011 to develop this guide.
Marc Janssens is with Southwest Research Institute.
Babrauskas, V., "Fire Modeling Tools for FSE: Are They Good Enough?" Journal of Fire Protection Engineering, vol. 8, pp. 87-96, 1996.
Wickström, U. and Göransson, U., "Full-Scale/Bench-Scale Correlations of Wall and Ceiling Linings," Fire and Materials, vol. 16, pp. 15-22, 1992.
Babrauskas, V., "Specimen Heat Fluxes for Bench-Scale Heat Release Rate Testing," Fire and Materials, vol. 19, pp. 243-252, 1995.
Mitler, H., "Predicting the Spread Rates of Fires on Vertical Surfaces," in Twenty-Third Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, PA, 1991, pp. 1715-1721.
Smith, E. and Green, T., "Release Rate Tests for a Mathematical Model," in Mathematical Modeling of Fires, ASTM STP 983, American Society for Testing and Materials, West Conshohocken, PA, 1987, pp. 7-20.
Dillon, S., Kim, W. and Quintiere J,, "Determination of Properties and the Prediction of the Energy Release Rate of Materials in the ISO 9705 Room-Corner Test," National Institute of Standards and Technology, Gaithersburg, MD, NIST-GCR-98-753, 1998.
Theuns, E., Merci, B., Vierendeels, J. and Vandevelde, P., "Extension and Evaluation of the Integral Model for Transient Pyrolysis of Charring Materials," Fire and Materials, vol. 29, pp. 195–212, 2005,
Lautenberger, C., "A Generalized Pyrolysis Model for Combustible Solids." Ph.D. Thesis, University of California Berkeley, 2007.
ASTM E 1591, American Society for Testing and Materials, West Conshohocken, PA, 2007.
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